Question

A rectangular room that is 3 feet longer than it is wide has area of 54 square feet how many feet long is the room

Answer 1

The room is 9 feet long.

Explanation:

Lets take the width of the room as
`x` feet.

Then, the length of the room will be
`x+3` feet.

Are of a rectangle = Length * Width

⇒
`54=x*(x+3)`

⇒
`54=x^(2) +3x`

⇒
`0=x^(2) +3x-54`

⇒
`x^(2) +3x-54=0`

⇒
`x^(2) +9x-6x-54=0`

⇒
`x(x+9)-6(x+9)=0`

⇒
`(x+9)(x-6)=0`

Thefore either,

`x+9=0` or
`x-6=0`

`x=-9` or
`x=6`

`x` is the width of the room, so a width cannot have a negative value. So we take the positive value.

Therefore,

`x=6` ⇒ Width of the room is 6 feet.

Length of the room =
`x+3` =
`6+3`=9 feet.

Therefore the room is 9 feet long.